Discussion Forum

If A and B are events having probabilities P(A)=0.6 , P(B)=0.4  and  $P(A\cap B)=0$ , then probability that neither  A nor B occurs is 

Answer:

Explanation:

Given, P(A)=0.6 , P(B)=0.4 and $P(A\cap B)=0$  then

P(neither A nor B)= $P(\overline{A}\cap \overline{B})$

= $P(\overline{A\cap B})=1-P(A\cup B)$

    = $1-P(A)-P(B)+P(A\cap B)$

              $[\because P(A\cup B)=P(A)+P(B)-P(A\cap B)]$

  =1-0.6-0.4+0=1-1=0